It is best to water plants with water that is at room temperature or ambient temperature. Cold water actually shocks plants and hot water can burn the roots of plants.
The specific heat of water is 4.186 Joules per gram degrees Celsius
(J/g degree C).
This means that it takes 4.186 Joules of energy (The joule is the unit of energy as cm or inch is a unit of length) to raise the temperature of 1 gram of water by one degree celsius. Basically, it takes more energy to heat water than to heat other substances like Iron, Lead and so on.
So, the short of the long of that is that with warm water, a lot of energy is stored in water and therefore, more energy is transferred to the soil and the roots of the plant and is able to heat up the soil.
Also, if you water with warm water and the temperature suddenly drops, the temperature of the water will be buffered against the cold and buffer the plant (protect the plant) from cold temperatures